I. Multiple Conceptual Contexts of Sound Perception

PSYCHOACOUSTICS: psychological, subjective perceptual analysis, awareness, and assignment of meaning (interpretation) relative to acoustical physical analysis; the scientific attempt to quantify qualitative experience and interpretation.

NEUROPSYCHOLOGY: psychological subjective/objective perceptual analysis, reaction, and assignment of meaning relative to neurological physical analysis. Subjective perceptual experience correlated with technological analysis.

ACOUSTICS: mathematical description and physical analysis of wavelength phenomena and relational dynamics. Inferred relationships examined between quantifiable data and objective (quantified) perception characteristics.

NEUROLOGY: anatomical description and physical analysis of sensory/motor impulse creation/transmission via the brain, spinal cord and nerves. Inferred relationships examined between quantifiable data and objective (quantified) perception characteristics and biological processes.

CYMATICS: physical analysis of the resonance pattern formation and dynamic form/motion effects of sound vibrations on inert matter and fluids. Specific elements include morphology and kinetics/dynamics in essential interrelation to acoustic vibration.

These phenomena can be conceptualized as a visible manifestation of 3D spatial harmonics. That is, sound wave spectra temporally structuring matter in space. Thus, blurring the conceptual boundaries between the visible and auditory segments of the electromagnetic spectrum.

characteristics of spatial harmonics:
Complex, spontaneous spatio-temporal organization of a sound wave/particle system.
Spontaneous self-organization
Reactive nonlinear ‘communicating’ system/process.
Pattern regularity
Currently, the (predominant) fundamental, isolated 1st harmonic is:
visible in 2 dimensions with Chladni and harmonograph patterns
visible in 3 dimensions with Cymascope images

Spatial harmonics can be appreciated, as an awareness of harmonically (overtones) derived energy (wave/particle) transformations, through their perceptible spatiotemporal effects on matter.

An analogy can be appreciated within dynamically complex polychromatic color perception (gestalt). Here, light wave harmonic spectra are temporally structuring the
visual perception (appearance) of matter in space. These subtle perceptions may only be appreciated indirectly as an overall gestalt shift as opposed to direct recognition of varying subcomponent wavelength elements. In this instance, there is a change in appearance without a corresponding change in structure.

i.e. subtle polychromatic [harmonic spectra] differentials of complex color combinations, where the metaphoric ‘fundamental’ frequency is the basic metacolor and the perceptible harmonic spectra (microcolors) are made of characteristic relative harmonic patterns of visible light in context.

MUSIC THEORY: perceptual analysis/codification of a music system nomenclature. Basic qualitative aspects of perception defined in an absolute, conventional notation system.

MUSIC CRITICISM/AESTHETICS: subjective qualitative perceptual analysis and interpretation of art.

ETHNOMUSICOLOGY: investigation of cultural aspects of musical perception, conception and appreciation. Analysis of psychosocial context: cultural influences and assumptions regarding pitch, tone, melody, harmony and rhythm, as well as traditional musical forms and aesthetic criteria. (i.e. consonance/dissonance, good/bad music etc.)

AUDIOLOGY: functional anatomic hearing perception measurement, evaluation and rehabilitation of impairment.

 II. Descriptive concepts involving primary musical elements

Pitch: fundamental or predominant sound frequency component within a unique gestalt harmonic spectra (timbre; tone color).

Frequency – mathematical measurement of pitch based on linear assumptions, relationships ‘by definition’ (ie octave = double or half the frequency). From a perceptual standpoint, while generally true on a macro, low-resolution level, anomalies emerge as pitch/interval resolution increases (theory/empirical mismatch).

Tone: gestalt composite perception of a fundamental pitch and its embedded, unique harmonic spectra (timbre; tone color).

Hertz (Hz): numerical frequency of sound wave cycles per second. Optimal human
audible range upper and lower limits are generally considered as 20Hz – 20KHz, based on
sine wave testing. The auditory system is more sensitive to frequencies in the range of 1 –
4 KHz.

Cents: 1/100 of a semitone, the logarithmic unit of measurement between intervals
enabling intervallic relationships to remain constant while Hz values change along a
different scale (i.e. yardstick/meterstick mismatch) relative to the actual component
pitches. So by definition, there are 1200 cents per octave, 100 cents per semitone
regardless of the frequency (Hz).

Example: if a record on a record player is slowed down the pitch changes (Hz) but the intervallic relationships (cents) of the melody and harmony stay the same.

Octave: defined numerically, in a fixed linear fashion as: 2 x frequency or 1/2 x
frequency. Base on the fundamental premise of ‘octave equivalence’ which relies on an
assumption of a linear system (pitch perception is a nonlinear process). Also defined
alphabetically, as the repetition of a pitch name while progressing linearly through the
pitch sequence of a given temperament. Human audible range is roughly 10 octaves.

Pitch Name (note) – 7 repeating alphabetical (a,b,c,d,e,f,g) ‘white’ pitches with 5 flat/
sharp ‘black’ modifiers, each semitone is 100 cents apart (piano color analogy).

Enharmonic: collapse of 2 pitches of a prior tuning system into 1 pitch with 2 names.
(ie. C# = Db)

Semitone: each discrete pitch within the octave of the 12ET tuning system (100 cents).

Microtone: generically, discrete pitch intervals with a value of less than 100 cents.

Macrotone: generically, discrete pitch intervals with a value of more than 100 cents.

Metapitch: a chromatic semitone which becomes subdivided in a higher resolution
microtonal temperament. i.e. metapitch ‘C’ becomes further divided into 4 micropitches in
48ET. This enables an efficient transition and expansion of musical systems without
reinventing the wheel or having numerous incompatible systems to learn, teach and

This conceptual distinction enables backward compatibility with former chromatic
pitch systems. i.e. metapitch ‘C’ subdivided into colored micropitches:

Cr [red], Co [orange], Cy [yellow], Cg [green], [blue], Cv [violet], etc…

Micropitch: increased auditory resolution subdivisions of a metapitch, notated polychromatically with colored noteheads.

Interval: the fixed ratio of two pitch frequencies (semitones, macro/microtones). Traditionally, modally defined and named (2nd, 3rd, 7th etc.) with major/minor/augmented/diminished modifiers; measured in cents.

Spectral Temperaments: the utilization of color to delineate delineate pitch color (fundamental-pitch spectra; polychromatic) and/or tone color (harmonics spectra) within a musical notation language.

Polychromatic: a music paradigm which includes all potential microtonal and macrotonal pitch ‘color’ palettes. All possible pitch palettes within this paradigm are conceived and expressed, both acoustically and visually, as various color schemes within the pitch continuum. Because it is an adaptable and relatively defined system, it is capable of notating more advanced musical aspects of pitched sound such as:nonlinear and/or linear interrelationships as well as dynamic and contextual pitch relativity)

The polychromatic system is an intuitive simplification of the extensive accumulation of
incompatible microtonal pitch modifier symbols within black and white, chromatic notation

It is an evolution of (mono)Chromatic; combinations and contrasts of black and white with
rudimentary embedded pitch/intervallic assumptions: static, absolute, acontextual, linear,
intervallic relationships.

Timbre: tone color; gestalt ‘sound’ quality characteristics of a fundamental pitch and its
integrated configuration/spectra of harmonics (i.e. harsh, complex, lush, hollow, brass-
like, etc…). Based partially on static and dynamic aspects of the relative frequency
spectrum, phase and temporal relationships, and intensity characteristics of the sound.
Additional deeper elements encompass interactive relationships in which the whole is
greater than the component elements (gestalt).

Tone Color: one or more pitch colors (i.e. C white, C orange) + harmonics = timbre
Pitch Color: specific spectral color designation of any micro/macropitch (higher/lower
aural resolution; i.e. C is the metapitch and o is the composer-defined micro/macropitch
designation); that is, the fundamental pitch without harmonics.

Dynamics: subjectively relative volume level expressed musically: pianissimo → mezzoforte → fortissimo, etc.

Amplitude: objectively determined volume level expressed in decibels (dB) relative to
sound pressure levels.
0 dB = threshold of hearing → 120 dB = threshold of pain.
dB levels over 85 dB can induce permanent hearing loss depending on duration or absolute transient peak level.

Volume: subjective perception of loudness; confusion of terminology with the scientific word volume (as in the volume of a container or space).

III. Segmented quantitative/qualitative Perspectives of Sound

Relative to sound perception via Peripheral Aural Acuity – physical aspects of the ear/cochlea and its relationship to biomechanically impeded perceptual problems such as frequency based hearing loss/hyperacusis, tone deafness, etc.
– audiology, otology and neurology

Relative to sound perception via Central Aural Acuity – physical aspects related to the
neural processing of peripheral auditory information in the brain via Cranial Nerve 8 (auditory nerve).
– neurology, neurotology and neuropsychology

Relative to objective quantifiable Physical Characteristics of sound – acoustics

Relative to objective Physical Effects of sound waves on matter – cymatics

Relative to subjective Perception, Understanding and Meaning of sound
– psychoacoustics, aesthetics

Relative to Musical Nomenclature and pedagogic organization of musical sound
– music theory

Relative to Historical and Cultural Aspects of musical sound
– musicology, ethnomusicology

Relative to Empirical Practice, Performance and Creation
– musician, composer, sound designer/engineer, software/hardware interface design

IV. Multiple Mathematical Representations of Pitch in Chromatic (12 tone) Equal Temperament

a. pitch is enumerated on various, incompatible scales:

cents (logarithmic scale):

A4             A#/Bb           B                  C                  C#                D

0 cents       100 cents       200 cents     300 cents     400 cents     500 cents

hertz/cycles per second (rounded):

440 Hz        466.36 Hz     493.88 Hz   523.25 Hz      554.37 Hz     587.33 Hz

MIDI note number

69                 70                 71               72                 73                   74

b. MIDI note number – Middle ‘C’ (C4) is set to a MIDI note number of 60. Adjacent pitches are numbered consecutively from this point with numbers decreasing as the pitch/note lowers and increasing as the pitch/note raises.

Limited to 128 note values per channel

c.  Scientific Pitch Notation: musical pitch range representation with numerical distinction of octaves.

C0, C#/Db0, D0 … A#/Bb0, B0

C9, C#/Db9, D9 … A#/Bb9, B9

d. Hexadecimal representation (0,1,2, …, 8,9,a,b,c,d,e,f).

Base 16 is used in representing the numerical relationships of computer science and programming, and is an integral element in the organization of the MIDI protocol and its musical definitions (i.e. pitch, volume, duration, etc).

Since hexadecimal numbers contain digits for 10 through 15, letters of the alphabet are used to represent those digits, starting at A = 10.

Hexadecimal numbers are often written with an h following them to distinguish them from decimal numbers: A4h indicates that A4 is a hexadecimal number.

e. Other numerical scales of pitch are in less universal use such as:

The mel pitch scale is used in psychoacoustic research and applications. The mel scale represents a perceptual scale of pitches generally judged to be equal in distance from one another by research subjects under experimental conditions. There are multiple mel scale formulas (no consistent absolute values, many subjective scales).